The Peano's parlour library

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Welcome to the library, our central repository for references cited here on Peano's parlour.

Library holdings

  1. Samuel Coskey and Roman Kossak. The complexity of classification problems for models of arithmetic. Bull. Symbolic Logic 16(3):345--358, 2010. www   MR   bibtex
  2. Grégory Duby. Automorphisms with only infinite orbits on non-algebraic elements. Arch. Math. Logic 42(5):435--447, 2003. www   DOI   MR   bibtex
  3. Fredrik Engström. A note on standard systems and ultrafilters. J. Symbolic Logic 73(3):824--830, 2008. www   DOI   MR   bibtex
  4. Harvey Friedman. One hundred and two problems in mathematical logic. J. Symbolic Logic 40:113--129, 1975. MR   bibtex
  5. Su Gao. Invariant descriptive set theory. Vol. 293, CRC Press, Boca Raton, FL, 2009. MR   bibtex
  6. Haim Gaifman. Models and types of Peano's arithmetic. Ann. Math. Logic 9(3):223--306, 1976. MR   bibtex
  7. Victoria Gitman. Scott's problem for proper Scott sets. J. Symbolic Logic 73(3):845--860, 2008. www   DOI   MR   bibtex
  8. Wilfrid Hodges. Building models by games. Vol. 2, Cambridge University Press, Cambridge, 1985. MR   bibtex
  9. Emil Jeřábek and Leszek Aleksander Kołodziejczyk. Real closures of models of weak arithmetic. Arch. Math. Logic 52(1-2):143--157, 2013. www   DOI   MR   bibtex
  10. Vladimir Kanovei. On "star" schemata of Kossak and Paris. Logic Colloquium '96 (San Sebastián)12:101--114, Berlin, 1998. MR   bibtex
  11. Matt Kaufmann. A rather classless model. Proc. Amer. Math. Soc. 62(2):330--333, 1977. MR   bibtex
  12. Matt Kaufmann and James H. Schmerl. Saturation and simple extensions of models of Peano arithmetic. Ann. Pure Appl. Logic 27(2):109--136, 1984. www   DOI   MR   bibtex
  13. Matt Kaufmann and James H. Schmerl. Remarks on weak notions of saturation in models of Peano arithmetic. J. Symbolic Logic 52(1):129--148, 1987. www   DOI   MR   bibtex
  14. Richard Kaye. A Galois correspondence for countable recursively saturated models of Peano arithmetic. Automorphisms of first-order structures, pp. 293--312, New York, 1994. MR   bibtex
  15. Richard Kaye, Roman Kossak and Henryk Kotlarski. Automorphisms of recursively saturated models of arithmetic. Ann. Pure Appl. Logic 55(1):67--99, 1991. www   DOI   MR   bibtex
  16. Richard Kaye and Tin Lok Wong. Truth in generic cuts. Ann. Pure Appl. Logic 161(8):987--1005, 2010. www   DOI   MR   bibtex
  17. Julia F. Knight. Hanf numbers for omitting types over particular theories. J. Symbolic Logic 41(3):583--588, 1976. MR   bibtex
  18. Julia Knight and Mark Nadel. Models of arithmetic and closed ideals. J. Symbolic Logic 47(4):833--840 (1983), 1982. www   DOI   MR   bibtex
  19. Friederike Körner. Automorphisms moving all non-algebraic points and an application to NF. J. Symbolic Logic 63(3):815--830, 1998. www   DOI   MR   bibtex
  20. Roman Kossak. A note on satisfaction classes. Notre Dame J. Formal Logic 26(1):1--8, 1985. www   DOI   MR   bibtex
  21. Roman Kossak. Models with the $\omega$-property. J. Symbolic Logic 54(1):177--189, 1989. www   DOI   MR   bibtex
  22. R. Kossak. Exercises in ‘back-and-forth’. Proceedings of the Nineth Easter Conference on Model Theory, Gosen, 1991. bibtex
  23. Roman Kossak. Four problems concerning recursively saturated models of arithmetic. Notre Dame J. Formal Logic 36(4):519--530, 1995. (Special Issue: Models of arithmetic) www   DOI   MR   bibtex
  24. Roman Kossak. A note on a theorem of Kanovei. Arch. Math. Logic 43(4):565--569, 2004. www   DOI   MR   bibtex
  25. Roman Kossak and Henryk Kotlarski. Game approximations of satisfaction classes and the problem of rather classless models. Z. Math. Logik Grundlag. Math. 38(1):21--26, 1992. www   DOI   MR   bibtex
  26. Roman Kossak and Henryk Kotlarski. More on extending automorphisms of models of Peano arithmetic. Fund. Math. 200(2):133--143, 2008. www   DOI   MR   bibtex
  27. Roman Kossak, Henryk Kotlarski and James H. Schmerl. On maximal subgroups of the automorphism group of a countable recursively saturated model of PA. Ann. Pure Appl. Logic 65(2):125--148, 1993. www   DOI   MR   bibtex
  28. Roman Kossak and Jeffrey B. Paris. Subsets of models of arithmetic. Arch. Math. Logic 32(1):65--73, 1992. www   DOI   MR   bibtex
  29. Roman Kossak and James H. Schmerl. Minimal satisfaction classes with an application to rigid models of Peano arithmetic. Notre Dame J. Formal Logic 32(3):392--398, 1991. www   DOI   MR   bibtex
  30. Roman Kossak and James H. Schmerl. The automorphism group of an arithmetically saturated model of Peano arithmetic. J. London Math. Soc. (2) 52(2):235--244, 1995. www   DOI   MR   bibtex
  31. Roman Kossak and James H. Schmerl. The structure of models of Peano arithmetic. Vol. 50, The Clarendon Press Oxford University Press, Oxford, 2006. (Oxford Science Publications) www   DOI   MR   bibtex
  32. Roman Kossak and James H. Schmerl. On cofinal extensions and elementary interstices. Notre Dame J. Formal Logic 53(3):267--287, 2012. www   bibtex
  33. Daniel Lascar. The small index property and recursively saturated models of Peano arithmetic. Automorphisms of first-order structures, pp. 281--292, New York, 1994. MR   bibtex
  34. George Mills. Substructure lattices of models of arithmetic. Ann. Math. Logic 16(2):145--180, 1979. www   DOI   MR   bibtex
  35. Ermek S. Nurkhaidarov. Automorphism groups of arithmetically saturated models. J. Symbolic Logic 71(1):203--216, 2006. www   DOI   MR   bibtex
  36. J. B. Paris. On models of arithmetic. Conference in Mathematical Logic---London '70 (Bedford Coll., London, 1970), pp. 251--280. Lecture Notes in Math., Vol. 255, Berlin, 1972. MR   bibtex
  37. J. B. Paris. Models of arithmetic and the 1-3-1 lattice. Fund. Math. 95(3):195--199, 1977. MR   bibtex
  38. John S. Schlipf. A guide to the identification of admissible sets above structures. Ann. Math. Logic 12(2):151--192. MR   bibtex
  39. James H. Schmerl. Peano models with many generic classes. Pacific J. Math. 46:523--536, 1973. MR   bibtex
  40. James H. Schmerl. Extending models of arithmetic. Ann. Math. Logic 14:89--109, 1978. www   DOI   MR   bibtex
  41. James H. Schmerl. Recursively saturated, rather classless models of Peano arithmetic. Logic Year 1979--80 (Proc. Seminars and Conf. Math. Logic, Univ. Connecticut, Storrs, Conn., 1979/80)859:268--282, Berlin, 1981. MR   bibtex
  42. James H. Schmerl. Recursively saturated models generated by indiscernibles. Notre Dame J. Formal Logic 26(2):99--105, 1985. www   DOI   MR   bibtex
  43. James H. Schmerl. Large resplendent models generated by indiscernibles. J. Symbolic Logic 54(4):1382--1388, 1989. www   DOI   MR   bibtex
  44. James H. Schmerl. Automorphism groups of models of Peano arithmetic. J. Symbolic Logic 67(4):1249--1264, 2002. www   DOI   MR   bibtex
  45. James H. Schmerl. Diversity in substructures. 361:145--161, Providence, RI, 2004. www   DOI   MR   bibtex
  46. James H. Schmerl. Nondiversity in substructures. J. Symbolic Logic 73(1):193--211, 2008. www   DOI   MR   bibtex
  47. James H. Schmerl. Elementary cuts in saturated models of Peano arithmetic. Notre Dame J. Form. Log. 53(1):1--13, 2012. www   DOI   MR   bibtex
  48. James H. Schmerl. Infinite substructure lattices of models of Peano arithmetic. J. Symbolic Logic 75(4):1366--1382, 2010. www   DOI   MR   bibtex
  49. James H. Schmerl. The automorphism group of a resplendent model. 51:647--649, 2012. www   DOI   MR   bibtex
  50. Dana Scott. Algebras of sets binumerable in complete extensions of arithmetic. Proc. Sympos. Pure Math., Vol. V, pp. 117--121, Providence, R.I., 1962. MR   bibtex
  51. Stuart T. Smith. Extendible sets in Peano arithmetic. Trans. Amer. Math. Soc. 316(1):337--367, 1989. www   DOI   MR   bibtex
  52. C. Smoryński. Elementary extensions of recursively saturated models of arithmetic. Notre Dame J. Formal Logic 22(3):193--203, 1981. www   MR   bibtex
  53. C. Smoryński. A note on initial segment constructions in recursively saturated models of arithmetic. Notre Dame J. Formal Logic 23(4):393--408, 1982. www   MR   bibtex
  54. A. J. Wilkie. On models of arithmetic having non-modular substructure lattices. Fund. Math. 95(3):223--237, 1977. MR   bibtex

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